A Hierarchical Bayesian Design for Phase I Trials of Novel Combinations of Cancer Therapeutic Agents

Summary We propose a hierarchical model for the probability of dose‐limiting toxicity (DLT) for combinations of doses of two therapeutic agents. We apply this model to an adaptive Bayesian trial algorithm whose goal is to identify combinations with DLT rates close to a prespecified target rate. We describe methods for generating prior distributions for the parameters in our model from a basic set of information elicited from clinical investigators. We survey the performance of our algorithm in a series of simulations of a hypothetical trial that examines combinations of four doses of two agents. We also compare the performance of our approach to two existing methods and assess the sensitivity of our approach to the chosen prior distribution.     

Object Grasping using the Minimum Variance Model

Reaching-to-grasp has generally been classified as the coordination of two separate visuomotor processes: transporting the hand to the target object and performing the grip. An alternative view has recently been formed that grasping can be explained as pointing movements performed by the digits of the hand to target positions on the object. We have previously implemented the minimum variance model of human movement as an optimal control scheme suitable for control of a robot arm reaching to a target. Here, we extend that scheme to perform grasping movements with a hand and arm model. Since the minimum variance model requires that signal-dependent noise be present on the motor commands to the actuators of the movement, our approach is to plan the reach and the grasp separately, in line with the classical view, but using the same computational model for pointing, in line with the alternative view. We show that our model successfully captures some of the key characteristics of human grasping movements, including the observations that maximum grip size increases with object size (with a slope of approximately 0.8) and that this maximum grip occurs at 60–80% of the movement time. We then use our model to analyse contributions to the digit end-point variance from the two components of the grasp (the transport and the grip). We also briefly discuss further areas of investigation that are prompted by our model.     

Regional Context in the Alignment of Biological Sequence Pairs

Sequence divergence derives from either point substitution or indel (insertion or deletion) processes. We investigated the rates of these two processes both in protein and non-protein coding DNA. We aligned sequence pairs using two pair-hidden Markov models (PHMMs) conjoined by one silent state. The two PHMMs had their own set of parameters to model rates in their respective regions. The aim was to test the hypothesis that the indel mutation rate mimics the point mutation rate. That is, indels are found less often in conserved regions (slow point substitution rate) and more often in non-conserved regions (fast point substitution rate). Both polypeptides and rRNA molecules in our data exhibited a clear distinction between slow and fast rates of the two processes. These two rates served as surrogates to conserved and non-conserved secondary structure components, respectively. With polypeptides we found both the fast indel rate and the fast replacement rate were co-located with hydrophilic residues. We also found that the average concordance, of our alignments with corresponding curated alignments, improves markedly when the model allows either of the two fast rates to colocate with hydrophilic residues. With rRNA molecules, our model did not detect colocation between the fast indel rate and the fast substitution rate. Nevertheless, coupling the indel rates with the point substitution rates across the two regions markedly increased model fit. This result suggests that rRNA pairwise alignments should be modeled after allowing for the two processes to vary simultaneously and independently in the two regions.     

Identification of conserved protein complexes based on a model of protein network evolution

MOTIVATION: Data on protein-protein interactions (PPIs) are increasing exponentially. To date, large-scale protein interaction networks are available for human and most model species. The arising challenge is to organize these networks into models of cellular machinery. As in other biological domains, a comparative approach provides a powerful basis for addressing this challenge. RESULTS: We develop a probabilistic model for protein complexes that are conserved across two species. The model describes the evolution of conserved protein complexes from an ancestral species by protein interaction attachment and detachment and gene duplication events. We apply our model to search for conserved protein complexes within the PPI networks of yeast and fly, which are the largest networks in public databases. We detect 150 conserved complexes that match well-known complexes in yeast and are coherent in their functional annotations both in yeast and in fly. In comparison with two previous approaches, our model yields higher specificity and sensitivity levels in protein complex detection. AVAILABILITY: The program is available upon request.     

Recovering Quasi-Active Properties of Dendritic Neurons from Dual Potential Recordings

We develop the theory and accompanying algorithm for the recovery of a dendritic neuron's cytoplasmic resistivity, membrane capacitance, leakage conductance, and two maximal channel conductances from weighted averages of simultaneous recordings of somatic and dendritic potential following a somatic current stimulus. We test our results on two model systems with distinct, though prescribed, channel kinetics and branching patterns.     

Genomic imprinting of two antagonistic loci

We present a model that considers the coevolution of genomic imprinting at a growth factor locus and an antagonistic growth suppressor locus. With respect to the two loci considered independently, our model makes the familiar predictions that an imprinted growth factor locus will only be expressed from the paternally derived allele and an imprinted growth suppressor locus only from the maternally derived allele. In addition, our coevolutionary model allows us to make predictions regarding the sequence of evolutionary events necessary for generating such a system. We conclude that imprinting at the growth factor locus preceded the evolution of growth suppressor function at the second locus, which in turn preceded imprinting at that locus. We then discuss the consistency of these predictions with currently available comparative data on the insulin-like growth factor 2 insulin-like growth factor 2 receptor system of mammals.     

The Determination of Relative Elemental Growth Rate Profiles from Segmental Growth Rates (A Methodological Evaluation)

Relative elemental growth rate (REGR) profiles describe spatial patterns of growth intensity; they are indispensable for causal growth analyses. Published methods of REGR profile determination from marking experiments fall in two classes: the profile is either described by a series of segmental growth rates, or calculated as the slope of a function describing the displacement velocities of points along the organ. The latter technique is usually considered superior for theoretical reasons, but to our knowledge, no comparative methodological study of the two approaches is currently available. We formulated a model REGR profile that resembles those reported from primary roots. We established the displacement velocity profile and derived growth trajectories, which enabled us to perform hypothetical marking experiments on the model with varying spacing of marks and durations of measurement. REGR profiles were determined from these data by alternative methods, and results were compared to the original profile. We find that with our model plotting of segmental relative growth rates versus segment position provides exact REGR profile estimations, if the initial segment length is less than 10% of the length of the whole growing zone, and if less than 20% of the growing zone is displaced past its boundary during the measurement. Based on our analysis, we discuss systematic errors that occur in marking experiments.     

A computational model of chemotaxis-based cell aggregation

We present a computational model that successfully captures the cell behaviors that play important roles in 2-D cell aggregation. A virtual cell in our model is designed as an independent, discrete unit with a set of parameters and actions. Each cell is defined by its location, size, rates of chemoattractant emission and response, age, life cycle stage, proliferation rate and number of attached cells. All cells are capable of emitting and sensing a chemoattractant chemical, moving, attaching to other cells, dividing, aging and dying. We validated and fine-tuned our in silico model by comparing simulated 24-h aggregation experiments with data derived from in vitro experiments using PC12 pheochromocytoma cells. Quantitative comparisons of the aggregate size distributions from the two experiments are produced using the Earth Mover's Distance (EMD) metric. We compared the two size distributions produced after 24 h of in vitro cell aggregation and the corresponding computer simulated process. Iteratively modifying the model's parameter values and measuring the difference between the in silico and in vitro results allow us to determine the optimal values that produce simulated aggregation outcomes closely matched to the PC12 experiments. Simulation results demonstrate the ability of the model to recreate large-scale aggregation behaviors seen in live cell experiments.     

Statistical alignment of retropseudogenes and their functional paralogs

We describe a model for the sequence evolution of a processed pseudogene and its paralog from a common protein-coding ancestor. The model accounts for substitutions, insertions, and deletions and combines nucleotide- and codon-level mutation models. We give a dynamic programming method for calculating the likelihood of homology between two sequences in the model and describe the accompanying alignment algorithm. We also describe how ancestral codons can be computed when the same gene produced multiple pseudogene homologs. We apply our methods to the evolution of human cytochrome c.     

Multiple interval mapping for gene expression QTL analysis

To find the correlations between genome-wide gene expression variations and sequence polymorphisms in inbred cross populations, we developed a statistical method to claim expression quantitative trait loci (eQTL) in a genome. The method is based on multiple interval mapping (MIM), a model selection procedure, and uses false discovery rate (FDR) to measure the statistical significance of the large number of eQTL. We compared our method with a similar procedure proposed by Storey et al. and found that our method can be more powerful. We identified the features in the two methods that resulted in different statistical powers for eQTL detection, and confirmed them by simulation. We organized our computational procedure in an R package which can estimate FDR for positive findings from similar model selection procedures. The R package, MIM-eQTL, can be found at .     

Maintaining phase of the crustacean tri-phasic pyloric rhythm

We construct and analyze a model network of the pyloric rhythm of the crustacean stomatogastric ganglion consisting of an oscillator neuron that inhibits two reciprocally inhibitory follower neurons. We derive analytic expressions that determine the phase of firing of the follower neurons with respect to the oscillator. An important aspect of the model is the inclusion of synapses that exhibit short-term synaptic depression. We show that these type of synapses allow there to be a complicated relationship between the intrinsic properties of the neurons and the synapses between them in determining phase relationships. Our analysis reveals the circumstances and ranges of cycle periods under which these properties work in concert with or independently from one another. In particular, we show that phase maintenance over a range of oscillator periods can be enhanced through the interplay of the two follower neurons if the synapses between these neurons are depressing. Since our model represents the core of the oscillatory pyloric network, the results of our analysis can be compared to experimental data and used to make predictions about the biological network.     

Modeling allosteric signal propagation using protein structure networks

Allosteric communication in proteins can be induced by the binding of effective ligands, mutations or covalent modifications that regulate a site distant from the perturbed region. To understand allosteric regulation, it is important to identify the remote sites that are affected by the perturbation-induced signals and how these allosteric perturbations are transmitted within the protein structure. In this study, by constructing a protein structure network and modeling signal transmission with a Markov random walk, we developed a method to estimate the signal propagation and the resulting effects. In our model, the global perturbation effects from a particular signal initiation site were estimated by calculating the expected visiting time (EVT), which describes the signal-induced effects caused by signal transmission through all possible routes. We hypothesized that the residues with high EVT values play important roles in allosteric signaling. We applied our model to two protein structures as examples, and verified the validity of our model using various types of experimental data. We also found that the hot spots in protein binding interfaces have significantly high EVT values, which suggests that they play roles in mediating signal communication between protein domains.     

Modeling the Spontaneous Activity of the Auditory Cortex

We present a rate model of the spontaneous activity in the auditory cortex, based on synaptic depression. A Stochastic integro-differential system of equations is derived and the analysis reveals two main regimes. The first regime corresponds to a normal activity. The second regime corresponds to epileptic spiking. A detailed analysis of each regime is presented and we prove in particular that synaptic depression stabilizes the global cortical dynamics. The transition between the two regimes is induced by a change in synaptic connectivity: when the overall connectivity is strong enough, an epileptic activity is spontaneously generated. Numerical simulations confirm the predictions of the theoretical analysis. In particular, our results explain the transition from normal to epileptic regime which can be induced in rats auditory cortex, following a specific pairing protocol. A change in the cortical maps reorganizes the synaptic connectivity and this transition between regimes is accounted for by our model. We have used data from recording experiments to fit synaptic weight distributions. Simulations with the fitted distributions are qualitatively similar to the real EEG recorded in vivo during the experiments. We conclude that changes in the synaptic weight function in our model, which affects excitatory synapses organization and reproduces the changes in cortical map connectivity can be understood as the main mechanism to explain the transitions of the EEG from the normal to the epileptic regime in the auditory cortex. D.H is incumbent to the Hass Russell Career Chair Development.     

Discrete stochastic models for compliance analysis based on an AIDS Clinical Trial Group (ACTG) study

Compliance is the extent to which a patient follows the prescribed regimen. Here we investigate the statistical properties of two popular measures of compliance - percentage of compliant days and percentage of doses taken. We use a stationary Markov chain to model the dependence structure of successive data points for each subject. We illustrate our model using discrete compliance data collected from an AIDS Clinical Trial Group study (ACTG 398). We check the model assumptions and evaluate the small sample as well as large sample properties of our estimators. We show that ignoring the within-subject dependence will usually underestimate the standard errors of the estimates of these compliance measures. Our model allows the application of meta-analytic approaches to assess the variation across subjects in these compliance indices and changes in them due to intervention.     

Protein engineering study of protein L by simulation.

We examine the ability of our recently introduced minimalist protein model to reproduce experimentally measured thermodynamic and kinetic changes upon sequence mutation in the well-studied immunoglobulin-binding protein L. We have examined five different sequence mutations of protein L that are meant to mimic the same mutation type studied experimentally: two different mutations which disrupt the natural preference in the beta-hairpin #1 and beta-hairpin #2 turn regions, two different helix mutants where a surface polar residue in the alpha-helix has been mutated to a hydrophobic residue, and a final mutant to further probe the role of nonnative hydrophobic interactions in the folding process. These simulated mutations are analyzed in terms of various kinetic and thermodynamic changes with respect to wild type, but in addition we evaluate the structure-activity relationship of our model protein based on the phi-value calculated from both the kinetic and thermodynamic perspectives. We find that the simulated thermodynamic phi-values reproduce the experimental trends in the mutations studied and allow us to circumvent the difficult interpretation of the complicated kinetics of our model. Furthermore, the level of resolution of the model allows us to directly predict what experiments seek in regard to protein engineering studies of protein folding--namely the residues or portions of the polypeptide chain that contribute to the crucial step in the folding of the wild-type protein.     

A statistical test for differences in sexual dimorphism between populations

Many studies involve comparison of measures of sexual dimorphism between two samples. This comparison is used to test a variety of hypotheses, such as changing environmental conditions. Methods for testing the significance of the difference between two populations tend to be complex, and/or require access to complete original data. We offer a simplified approach which is based on a linear regression model using dummy variables. Our method is computationally simple and can be used with summary statistics (sample size, means, standard deviations) instead of raw data. We present three examples of the application of our method to problems in physical anthropology. We also note that our method has a broader range of applications apart from that of sexual dimorphism.     

Seeing strangers or announcing "danger": galectin-3 in two models of innate immunity

Recent investigations on the molecular mechanisms by which our immune system recognizes infections and initiates defense against those infections have led to the proposition of two models explaining the way our innate immunity system functions; the self-nonself model and the Danger model. In this review, the roles of galectin-3 in innate immunity against infections--host-pathogen interactions--will be discussed. We will shed light on the potential contribution of a beta-galactoside binding mammalian lectin, galectin-3 as a molecule implicated in innate immunity from the angle of both the self-nonself model and the Danger model.     

QTL methodology for response curves on the basis of non-linear mixed models, with an illustration to senescence in potato

The improvement of quantitative traits in plant breeding will in general benefit from a better understanding of the genetic basis underlying their development. In this paper, a QTL mapping strategy is presented for modelling the development of phenotypic traits over time. Traditionally, crop growth models are used to study development. We propose an integration of crop growth models and QTL models within the framework of non-linear mixed models. We illustrate our approach with a QTL model for leaf senescence in a diploid potato cross. Assuming a logistic progression of senescence in time, two curve parameters are modelled, slope and inflection point, as a function of QTLs. The final QTL model for our example data contained four QTLs, of which two affected the position of the inflection point, one the senescence progression-rate, and a final one both inflection point and rate.